Question

Consider the simultaneous equations
\[ 2x + 4y = -7; \quad 3x + 5y = 1 \] While solving using Gauss elimination without pivoting, after the forward elimination, the diagonal elements of the coefficient matrix are

• A. 2 and -1
• B. 3 and 2
• C. 5 and -2
• D. 3 and 4

Hint:

Eliminate x from the second equation using the first row's pivot, then look at the resulting coefficient of y.

Answer 1

The Correct Option is A

Gauss elimination without pivoting simply uses the rows in the order given, so checking each option against a direct row reduction settles this.

1. Option (A) 2 and -1: correct, this comes from keeping row 1 as $[2, 4]$ and replacing row 2 with row 2 minus $1.5$ times row 1, which zeroes the first entry and turns $5$ into $-1$.
2. Option (B) 3 and 2: wrong, these are just the original first entries of row 1 and row 2 with no elimination applied.
3. Option (C) 5 and -2: wrong, $5$ is the untouched original second entry of row 2, and $-2$ does not come from the correct multiplier.
4. Option (D) 3 and 4: wrong, these numbers mix entries from different rows without performing any elimination step.

Working the elimination directly: the multiplier is $3/2$, so new row 2 is $[3 - 1.5(2), \ 5 - 1.5(4)] = [0, -1]$. The coefficient matrix ends up upper triangular with diagonal $2$ and $-1$, so option (A) is correct.